Chaos Theory

The entire Universe seems to be filled with randomness and chaos. Most of us are susceptible to this half-truth. Chaos theory sheds light on this half-truth. It opens up an entirely new realm of probability and order even during the most chaotic phenomena in nature.

What is Chaos Theory?

Chaos theory is the extensive study of evidently random or uncertain behaviour in bodies or events controlled by deterministic laws. Deterministic chaos is a more accurate term which suggests a paradox as it links two concepts that are familiar and generally considered incompatible. The primary notion is that of unpredictability or randomness, as in the path of a gas molecule, and in the voting pattern of a person from out of a certain population section. In conventional examinations, randomness was considered more apparent than something real. It came from the ignorance of numerous causes involved. Specifically, it was common to believe that the entire Universe is unpredictable because it is sophisticated and complex in all senses. The second is about deterministic motion, such as that of a planet or a pendulum, which has been believed to be true since the Isaac Newton era as illustrating the success of science in processing predictable phenomena which are initially complex.

Chaos theory explains that within the visible randomness of complex, chaotic systems, there are inherent repetition, patterns, self-organisation, interconnectedness, self-similarity, and constant feedback loops. The butterfly effect is an underlying aspect of chaos. It explains how a small fluctuation in one condition of a nonlinear deterministic system can generate a huge difference in the later outcomes. It means that there is delicate dependence on beginning states. A classic metaphor for this nature is that a crow flapping its wings in India can cause a typhoon in Tokyo.

History of Chaos Theory

Henri Poincaré was the prominent pioneer of chaos theory. During the 1880s, he studied the three-body problem and discovered that there is a chance of orbits having a nonperiodic nature. However, it is not yet forever increasing nor approaching a constant point. In 1898, Jacques Hadamard presented a study about a potent analysis of the chaotic motion of free particles gliding frictionlessly on the surface of constant negative curvature known as the “Hadamard dynamical system”. He was able to explain that every trajectory is unstable in that all particle paths diverge and separate exponentially from each other, along with a positive Lyapunov exponent. The major catalyst for the evolution of chaos theory was the development of the electronic computer. The primary mathematics of chaos theory consists of the repeated iteration of mathematical equations, which would be not practical to do by hand. The accurate computational ability of electronic computers allowed us to solve these recursive calculations, while images and figures made it easy to visualise these systems.

Applications of Chaos Theory

Even though chaos theory was originally derived from analysing weather patterns, it has been applicable to many other situations. Some fields utilising chaos theory are computer science, geology, engineering, meteorology, physics, population dynamics, robotics, biology, anthropology, mathematics, politics, philosophy and economics. With time, many fields started applying chaos theory as probability and uncertainty are crucial in almost every scientific field.

Chaos theory has been effectively applied to anticipate the long-term behaviour of various biological phenomena and systems using the method called “Recurrence Plot”. This technique of application should even be useful in Systems Engineering. Recurrence plots disclose emergent and long-term behaviour in complicated systems when particular criteria are met. This method may be applied in Systems Engineering in such different fields as Systems Architecture to forecast emergent behaviours in Complex Systems and also Program Management to deduce the long-term well-being of complex projects, among others.

The video about the fundamentals of weather forecasting

What is the Butterfly Effect?

The butterfly effect is defined as the sensitive dependence on the starting conditions in which a slight variation in one condition of a nonlinear deterministic system can generate huge differences in the later outcomes. The concept is closely related to the work of Edward Norton Lorenz. He discovered that the deterministic exposition of the Universe could not account for the lack of accuracy in human calculation of natural phenomena. He noticed that the Universe’s interdependent cause-and-effect connections are too sophisticated to resolve. To deduce the most probable outcomes for such sophisticated systems as weather sequences, he started employing groups of slightly varied starting states to perform parallel meteorological simulations. This technique is still utilised presently to produce daily weather predictions. Weather is the most familiar phenomenon associated with the butterfly effect.

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